1. Field of the Invention
The present invention is directed to a magnetic resonance apparatus of the type having a basic field magnet system for generating a basic magnetic field and a gradient coil system with a coil arrangement, wherein the curvature of a conductor of the coil arrangement with current flowing therein is set for generating a predetermined target magnetic field using a method that takes linear secondary conditions into consideration.
2. Description of the Prior Art
Magnetic resonance tomography is a known technique for generating images of the internal body of an examination subject. To that end, in a magnetic resonance tomography apparatus rapidly switched gradient fields are superimposed on a static basic magnetic field that is generated by a basic field magnet system, the gradient fields being generated by a gradient coil system composed of primary and secondary coils. Further, the gradient coil system often includes shim coils with which the homogeneity of the basic magnetic field can be improved. Further, the magnetic resonance tomography apparatus has a radio-frequency system that emits radio-frequency signals into the examination subject for triggering magnetic resonance signals. The radio-frequency system also registers the generated magnetic resonance signals from which magnetic resonance images are produced.
For generating gradient fields, suitable, predetermined currents are supplied to the gradient coils. The current rise and decay rates amount to several 100 kA/s. Given an existing basic magnetic field on the order of magnitude of 1 T, Lorentz forces that lead to oscillations of the gradient coil system act on these time-variable currents in the gradient coils. These oscillations are transmitted to the surface of the apparatus via various propagation paths. The surface converts these mechanical oscillations into acoustic oscillations that ultimately lead to inherently unwanted noise.
An analysis of the aforementioned oscillations can be based, for example, on the natural resonant behavior of the gradient coil system. The natural resonance behavior is defined by the eigenfrequencies and the eigenfrequency modes. The effect of the Lorentz forces on the eigenfrequency modes is described in the form of participation factors. These indicate the extent to which the Lorentz forces excite a specific eigenfrequency mode. Given knowledge of the participation factors and the eigenfrequencies, the oscillation of the gradient coil system can be defined for every location and for each frequency for superimposing the oscillations of the natural resonant modes.
German OS 42 03 582, corresponding to U.S. Pat. No. 5,309,107, discloses a transverse gradient coil wherein the coil conductors are arranged on a carrier and proceed on paths whose attachment points are defined in that a grid mesh network of elementary coils is placed over the carrier, the magnetic field produced by each elementary coil is calculated, and a number of Ampere turns is defined with a fit algorithm on the basis of a prescribable target field distribution for every elementary coil. Discrete conductor positions that serve as attachment points for the paths of the coil conductors are determined by integration. By introducing physical boundary conditions, a reduction in noise can thereby be achieved by minimizing global bending forces and an optimization of the mechanical oscillatory behavior can be achieved by minimizing reaction forces between the gradient coil and a basic field magnet system. To this end, a field component of the gradient coil that is critical for producing the Lorentz forces is minimized at the location of the basic field magnet system on the basis of a suitable boundary condition.
Further, German OS 197 26 332 discloses a coil arrangement that generates a predetermined target magnetic field wherein a specific number of constituent points in that current-carrying conductors in a layer of the coil arrangement proceed on paths whose supporting points are identified according to the following method:
For designing a coil arrangement, a layer in which conductors of the coil arrangement should proceed is first divided into a number of elementary surfaces adjoining one another. The aforementioned elementary surfaces are referred to in brief below as meshes. As a result of the classification, a network of meshes arises. The individual meshes, for example, are consecutively numbered for a hollow-cylindrical coil system according to FIG. 2, being numbered from 1 through Ñ. Thus, j=1 . . . N . . . N is valid for an appertaining running variable j.
Each of the aforementioned meshes can be considered as being surrounded by a conductor, so that a number of elementary coils conceptually arises, each being respectively composed of a closed winding. The current distribution on the entire conductor structure in the optimization is interpreted as the superimposition of closed, elementary circuits in the elementary coils. These are referred to below as mesh currents.
Further, a target magnetic field column vector z (gradient field or shim characteristic) is predetermined in a number M of constituent points Pi. The number M of constituent points is greater than the number Ñ of meshes. The appertaining running variable, with i is i=1 . . . M. The target magnetic field column vector z, which contains a number M of target fields z1 through ZM in the constituent points P1 through PM, normally contains constituent points on a surface of a sphere and constituent points on eddy current surfaces. The target magnetic field should be zero for the latter.
A unit current is considered as flowing in each of the Ñ elementary coils. A magnetic field contribution fij in each of the M constituent points that is generated by the appertaining unit current is thus obtained for each mesh. The contribution fij is thus the magnetic field contribution of a unit current in the jth mesh in the ith constituent point. The following magnetic field column vector b with the elements b1 through bM is obtained for a mesh current column vector i having the elements i1 through iÑ:       b    _    =            [                                                  b              1                                                            ⋮                                                              b              M                                          ]        =                            F          _                ·                  i          _                    =                        [                                                                      f                  11                                                            ⋯                                                              f                                      1                    ⁢                                          N                      ~                                                                                                                          ⋮                                            ⋰                                            ⋮                                                                                      f                  M1                                                            ⋯                                                              f                                      M                    ⁢                                          N                      ~                                                                                                    ]                ·                  [                                                                      i                  1                                                                                    ⋮                                                                                      i                                      N                    ~                                                                                ]                    
or, presented differently:       b    i    =            ∑              j        =        1                    N        ~              ⁢          xe2x80x83        ⁢                  f        ij            ·                        i          j                .            
A deviation of the magnetic field column vector b from the target magnetic field column vector z derives from:       ∑    i    ⁢      xe2x80x83    ⁢                    (                              b            i                    -                      z            i                          )            2        .  
A goal of an optimization is always a minimization of the aforementioned deviation. As disclosed in the aforementioned published German application, additional expressions to be minimized, for example the magnetic field energy multiplied by a weighting factor can thereby be added to the deviation, and, given employment of the described optimization algorithms, additional, linear secondary conditions having the form       "LeftBracketingBar"                  A        _            ·              i        _              "RightBracketingBar"    =                              [                                                                      a                  11                                                            ⋯                                                              a                                      i                    ⁢                                          N                      ~                                                                                                                          ⋮                                            ⋰                                            ⋮                                                                                      a                                      μ                    ⁢                                          xe2x80x83                                        ⁢                    1                                                                              ⋯                                                              a                                      u                    ⁢                                          N                      ~                                                                                                    ]                ·                  [                                                                      f                  11                                                                                    ⋮                                                                                      f                  M1                                                              ]                    ≤              [                                                            u                1                                                                        ⋮                                                                          u                μ1                                                    ]              =          u      _      
are made, wherein u is a prescribable limit column vector having the elements u1 through uxcexc and A is a prescribable matrix having the elements a11 through axcexcÑ for defining relations appertaining to the mesh currents. Examples thereof are described in the aforementioned published application.
The current distribution determined in this manner, i.e. the mesh current column vector i, is simulated with discrete conductors that are permeated by a constant rated current. Techniques for this are disclosed in the aforementioned published application.
Given the coil arrangement disclosed in the aforementioned published application, a disadvantage, among other things, is that factors regarding noise reduction do not enter into the design.
It is an object of the present invention to provide a magnetic resonance apparatus of the type initially described wherein the aforementioned disadvantages are avoided.
The above object is achieved in accordance with the principles of the present invention in a magnetic resonance apparatus of the type described above, and a method for designing a gradient coil system for a magnetic resonance apparatus, wherein the course or path of a current-carrying conductor of the coil arrangement for generating a predetermined target magnetic field is determined according to a method that allows linear secondary conditions to be taken into consideration, and wherein a noise-causing mechanical oscillation of the coil system, resulting from Lorentz forces acting on the current-carrying conductor in the basic magnetic field, is taken into consideration by one of the aforementioned linear secondary conditions, and the determination of the course or path of the current-carrying conductor is augmented so that the noise-causing oscillation is reduced.
Because one of the linear secondary conditions takes into account a noise-causing, mechanical oscillation of the coil system as a consequence of Lorentz forces that act on the current-permeated conductor in the basic magnetic field, the course of the conductor is additionally defined by the method so that the noise-causing oscillation is reduced. Thus, a noise-optimized coil system can be planned from the design outset without iterative intermediate steps.
In an embodiment, the oscillation to be diminished is at least one natural resonant mode of the coil system. Particularly given excitation of a dominant resonant mode, especially bothersome noise occurs as a consequence of the Lorentz forces, and therefore if this dominant mode is suppressed by the inventive method and apparatus, a significant noise reduction is achieved.
In another embodiment, the coil system is hollow-cylindrically fashioned, and the oscillation to be diminished has a component that is directed radially relative to a principal axis of the hollow cylinder. Since, given a hollow-cylindrical coil system, it is particularly the movements acting radially relative to the principal cylinder axis that are relevant to the noise, a high noise-reducing effect is thereby achieved given a simultaneous simplification of the method.
In a further embodiment, the method is a quadratic optimization containing a quadratic target function. As a result thereof, the method can be implemented in an especially advantageous way on a computer system in a forward calculation without iterative procedures.